Module 5 : Force Method - Introduction and applications
Lecture
3 : Analysis of Statically Indeterminate Structures by Energy Method
Example 5.15 The free ends of two cantilever beams each of length L and flexural rigidity EI are joined together with a spring as shown in Figure 5.18(a). The stiffness of the spring is . Determine the force in the spring due to a concentrated load W acting at center of the lower cantilever.
Solution: Let the force in the spring be R as shown in Figure 5.18(b). According to the Castigliano's theorem
where U is the total strain energy stored in the system.
. Determine the force in the spring due to a concentrated load W acting at center of the lower cantilever. 
and
